Consider a really long cylindrical capacitor with length l, which consists of two coaxially aligned cylindrical conductors, an inner massive tube with radius a and an outer hollow tube with inner radius b. The smaller con- ductor is charged with a surface charge density σ. By really long, we mean l ≫ a, b, or, for the application of Gauss’ law, we can assume the cylinder is infinitely long.

1. (a)  Draw both conductors, the location of σ on the inner conductor, the location of the induced charges on the outer conductor, the electric field between the conductors, and your choice of coordinate system

2. (b)  Use Gauss’ law to calculate the electric field in between the conduc- tors. Be explicit about all the fluxes through all of the parts of the Gaussian surface you have chosen.

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3. (c)  Calculate the potential difference V between the inner and outer conductors, make sure it is positive

4. (d)  Calculate the capacitance per unit length of this capacitor, i.e. C/l.

An electron is released a distance d away from the surface of a positively-

charged sphere with charge Q and radius r.

1. (a)  Calculate the velocity with which the electron strikes the sphere

2. (b)  If the electron is not initially at rest, but moving away at a velocity v, calculate the escape velocity, i.e. for which v the electron never turns around and strikes the sphere.